Truncated Icosahedron (rounded soccer form)
by mechadense, published
Well this is pretty much self explanatory.
Quite interesting math in there.
A cross-eyed 3D view of an explosion view is included in the images. You can watch it in full 3D without viewing aid. Just overlap the two almost identical looking sides sides by crossing your eyes. Note that you must first click it to view it un-cropped.
edit 2014-07-05: I've added modified version that can be assembled with 3mm diameter filament dowels.
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Print 20 hexagonal and 12 pentagonal pieces - then glue them together.
edit: The updated version can be put together with short pieces of 3mm diameter filament or other dowels.
Since it's OpenSCAD you can easily modify it to your liking.
Add a spiky surface; punch holes; attatch poles; whatever you like.